Nuclear medicine is a unique specialty wherein radiation is used to acquire images which show the function and anatomy of organs, bones or tissues of the body. The technique of acquiring nuclear medicine images entails first introducing radiopharmaceuticals into the body, either by injection or ingestion. These radiopharmaceuticals are preferentially taken up by specific organs, bones or tissues of interest (these exemplary organs, bones, or tissues are also more generally referred to herein using the term “objects”.) Upon arriving at their specified area of interest, the radiopharmaceuticals produce gamma photon emissions which emanate from the body and are then captured by a scintillation crystal. The interaction of the gamma photons with the scintillation crystal produces flashes of light which are referred to as “events.” Events are detected by an array of photo detectors (such as photomultiplier tubes) and their spatial locations or positions are then calculated and stored. In this way, an image of the organ or tissue under study is created from detection of the distribution of the radioisotopes in the body.
One particular nuclear medicine imaging technique is known as positron emission tomography, or PET. PET is used to produce images for diagnosing the biochemistry or physiology of a specific organ, tumor or other metabolically active site. The measurement of tissue concentration using a positron emitting radionuclide is based on coincidence detection of the two gamma photons arising from a positron annihilation. When a positron is annihilated by an electron, two 511 keV gamma photons are simultaneously produced and travel in approximately opposite directions. Gamma photons produced by an annihilation event can be detected by a pair of oppositely disposed radiation detectors capable of producing a signal in response to the interaction of the gamma photons with a scintillation crystal. Annihilation events are typically identified by a time coincidence between the detection of the two 511 keV gamma photons in the two oppositely disposed detectors (i.e., the gamma photon emissions are detected virtually simultaneously by each detector). When two oppositely disposed gamma photons each strike an oppositely disposed detector to produce a time coincidence event, they also identify a line(s)-of-response (LOR) along which the annihilation event has occurred. An example of a PET method and apparatus is described in U.S. Pat. No. 6,858,847, which patent is incorporated herein by reference in its entirety.
After being sorted into parallel projections, the LOR defined by the coincidence events are used to reconstruct a three-dimensional distribution of the positron-emitting radionuclide within the patient. In two-dimensional PET, each 2D transverse section or “slice” of the radionuclide distribution is reconstructed independently of adjacent sections. In fully three-dimensional PET, the data are sorted into sets of LOR, where each set is parallel to a particular detector angle, and therefore represents a two dimensional parallel projection p(r, s, φ, θ) of the three dimensional radionuclide distribution within the patient—where “r” and “s” correspond to the radial and axial distances, respectively, of the LOR from the center of the projection view and “φ” and “θ” correspond to the azimuthal and polar angles, respectively, of the projection direction with respect to the z axis in (x, y, z) coordinate space (in other words, φ and θ correspond to a particular LOR direction).
Coincidence events are integrated or collected for each LOR and stored in a sinogram. In this format, a single fixed point in the emitter distribution f(x, y) traces a sinusoid in the sinogram. Each row of a sinogram contains the LOR data for a particular azimuthal angle φ; each element of the row corresponds to a distinct radial offset of the LOR from the center of rotation of the projection. Different sinograms may have corresponded to projections of the tracer distribution at different coordinates along the scanner axis and/or different polar angles with respect to the scanner's axis.
FIG. 1 shows an embodiment of an exemplary PET system. A subject 4, for example a patient, is positioned within a detector ring 3 comprising photo-multiplier tubes (PMTs) 5. In front of the PMTs 5 are individual crystals 8, also called detectors 8. A group of four PMTs may have an array of detectors 8 in front of them. For example, an array of eight by eight or thirteen by thirteen detectors 8 (crystals) is possible, but any other array may be selected. Each detector 8 may be an individual crystal in front of respective PMT. As noted, during an annihilation process two photons 7 are emitted in diametrically opposing directions as schematically illustrated in circle 6. These photons 7 are registered by the PET as they arrive at detectors 8 in the detector ring 3. After the registration, the data, resulting from the photons 7 arriving at the detectors 8, may be forwarded to a processing unit 1 which decides if two registered events are selected as a so-called coincidence event. All coincidences are forwarded to the image processing unit 2 where the final image data may be produced via mathematical image reconstruction methods. The image processing unit 2 may be connected to a display for displaying one or more processed images to a user.
To accurately reconstruct PET data into a usable image, one must know the efficiencies of the detectors that collected them, in order to compensate for their variability. This is often done by placing a thin planar emission source producing negligible scatter in the scanner and comparing the measured responses along lines of response (LOR) normal to the source to the expected uniform responses. Clinical emission data inevitably include scattered radiation along with the unscattered true coincidences (“trues”), however. Scattered radiation and true coincidences are shown in FIG. 2. This scattered radiation may have angular and energy distributions different from those of the unscattered true coincidence photons, and therefore it is likely that the probability of detecting it will also be different from the trues. Because the relative amount and distribution of the scattered radiation varies with the object being imaged, its distinct detection efficiency must be accounted for separately from the trues efficiency.
If M represents a measured response for a detector pair forming an LOR, then neglecting random coincidences, M can be expressed in terms of the incident trues (T) and scattered (S) radiation as:M=εTT+∫ε(E,φ)S(E,φ)dEdφwhere εT and ε(E,φ) are the detection efficiencies for trues and scatter, respectively, and E and φ are the energy and incidence angle of the scattered radiation. Since there are two photons and two detectors involved for each LOR, the integral actually involves both energies and both incidence angles, but this is left implicit for notational simplicity.
We can write this equation in terms of the integral scatter flux S=∫S(E,φ)dEdφ asM=εTT+εSS 
where the average scatter efficiency for the LOR is:
      ε    S    =                    ∫                  ∈                                    (                              E                ,                ϕ                            )                        ⁢                          S              ⁡                              (                                  E                  ,                  ϕ                                )                                      ⁢                          ⅆ              E                        ⁢                          ⅆ              ϕ                                                  ∫                              S            ⁡                          (                              E                ,                ϕ                            )                                ⁢                      ⅆ            E                    ⁢                      ⅆ            ϕ                                .  
Because S(E, φ) is object dependent. εS may be also.
It is not obvious how one can determine εS directly since, for a source in the field of view (FOV) of the scanner, scatter is nearly always accompanied by true events. Ollinger proposed a partial solution to this problem in “Detector efficiency and compton scatter in full 3D PET,” IEEE Trans. Nuc. Sci., vol. 42, pp, 1168-1173, August 1995. He wrote the scatter detection efficiency (ηSijk in his notation) as the product of three components: the plane efficiency cSK, the detector efficiency εijk and the geometrical efficiency gijk:εS=ηijkS=ckSεijkgijk.
He proposed to use the same values of εijk for scatter as for trues, since he had no way of independently measuring them. He proposed to estimate the plane efficiencies by comparing measured to computed scatter in the tails of a sinogram of a uniform cylindrical phantom, although the scattered radiation in the tails may have a different energy and angular distribution than the scatter in the LORs passing through the object. He assumed gijk was equal to 1 everywhere, based on heuristic arguments. Finally, Ollinger treated ηSijk as object independent, and thus no components of it were included in the scatter simulation.
The approach to scatter normalization is different in the single scatter simulation (SSS) algorithm, as described in “New, faster, image-based scatter correction for 3D PET,” C. C. Watson, IEEE Trans. Nuc. Sci., vol. 47, pp. 1587-1594, August 2000, the entirety of which is incorporated by reference. From (2) the normalized measured (randoms corrected) data is:
                    1                  ε          T                    ⁢      M        =          T      +                                    ε            S                                ε            T                          ⁢        S              ,so the trues may be estimated by
      T    ^    =                    1                  ε          T                    ⁢      M        -                            (                                                    ε                S                                            ε                T                                      ⁢            S                    )                SSS            .      
Therefore scatter correction does not require independent knowledge of εS and εT, but only of their ratio. This is an advantage since first order effects in the variation of crystal efficiencies cancel out. The SSS algorithm includes an estimate of the detection efficiency of each simulated photon as a function of its energy and incidence angle. It also estimates the trues efficiency and forms their ratio so that the output of the SSS algorithm is an estimate of
                              ε          S                          ε          T                    ⁢      S        =                  1                  ε          T                    ⁢              ∫                              ε            ⁡                          (                              E                ,                ϕ                            )                                ⁢                      S            ⁡                          (                              E                ,                ϕ                            )                                ⁢                      ⅆ            E                    ⁢                      ⅆ            ϕ                                ,for the object-dependent scatter flux.
To the extent that this internal model is accurate, no separate normalization of the scatter is required. This model explicitly accounts for possible variations in the geometrical efficiency for scatter, and allows for its object dependence. There are limitations to this model, however, because it does not include an exact description of the detectors' structure. For example, although most modern PET scanners use pixelated block detectors, gaps that may exist between detector blocks are neglected in the model. These gaps may result in undesirable artifacts in the ultimate image.
It would be useful, therefore, to have a means of measuring and correcting for variations in the εs/εT ratio which is not accounted for in the simulation. Although there may be random residual variations in individual crystal intrinsic efficiency ratios, the focus is on the variations associated with the geometrical structure of the detectors, i.e. those that depend only on the location of the crystals within the block detector, and the location of the block detectors within the scanner. For a uniform ring scanner only one azimuthal projection angle needs to be considered, due to symmetry.